TR-2012002: Randomized Matrix Methods for Real and Complex Polynomial Root-Finding

To advance the known approach to univariate polynomial root-finding via computations in Frobenius matrix algebra, we incorporate some effective methods for matrix eigen-solving, randomized matrix algorithms, and subdivision techniques. We also develop iterations directed to the approximation of only real roots. Our analysis and experiments show effectiveness of the resulting numerical real and complex root-finders. Our auxiliary results on randomized matrix computations can be of independent interest.

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